### Abstract

Language | English |
---|---|

Pages | 89-110 |

Number of pages | 22 |

Journal | Louvain Economic Review |

Volume | 79 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2013 |

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### Keywords

- strategic market game
- bilateral oligopoly
- Cobb-Douglas preferences
- aggregative games

### Cite this

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*Louvain Economic Review*, vol. 79, no. 4, pp. 89-110. https://doi.org/10.3917/rel.794.0089

**On Cobb-Douglas preferences in bilateral oligopoly.** / Dickson, Alexander.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On Cobb-Douglas preferences in bilateral oligopoly

AU - Dickson, Alexander

PY - 2013

Y1 - 2013

N2 - Bilateral oligopoly is a simple model of exchange in which a finite set of sellers seek to exchange the goods they are endowed with for money with a finite set of buyers, and no price-taking assumptions are imposed. If trade takes place via a strategic market game bilateral oligopoly can be thought of as two linked proportional-sharing contests: in one the sellers share the aggregate bid from the buyers in proportion to their supply and in the other the buyers share the aggregate supply in proportion to their bids. The analysis can be separated into two `partial games'. First, fix the aggregate bid at $B$; in the first partial game the sellers contest this fixed prize in proportion to their supply and the aggregate supply in the equilibrium of this game is $\tilde{\mathcal X}(B)$. Next, fix the aggregate supply at $X$; in the second partial game the buyers contest this fixed prize in proportion to their bids and the aggregate bid in the equilibrium of this game is $\tilde{\mathcal B}(X)$. The analysis of these two partial games takes into account competition \emph{within} each side of the market. Equilibrium in bilateral oligopoly must take into account competition \emph{between} sellers and buyers and requires, for example, $\tilde{\mathcal B}(\tilde{\mathcal X}(B))=B$. When all traders have Cobb-Douglas preferences $\tilde{\mathcal X}(B)$ does not depend on $B$ and $\tilde{\mathcal B}(X)$ does not depend on $X$: whilst there is competition within each side of the market there is no strategic interdependence \emph{between} the sides of the market. The Cobb-Douglas assumption provides a tractable framework in which to explore the features of fully strategic trade but it misses perhaps the most interesting feature of bilateral oligopoly, the implications of which are investigated.

AB - Bilateral oligopoly is a simple model of exchange in which a finite set of sellers seek to exchange the goods they are endowed with for money with a finite set of buyers, and no price-taking assumptions are imposed. If trade takes place via a strategic market game bilateral oligopoly can be thought of as two linked proportional-sharing contests: in one the sellers share the aggregate bid from the buyers in proportion to their supply and in the other the buyers share the aggregate supply in proportion to their bids. The analysis can be separated into two `partial games'. First, fix the aggregate bid at $B$; in the first partial game the sellers contest this fixed prize in proportion to their supply and the aggregate supply in the equilibrium of this game is $\tilde{\mathcal X}(B)$. Next, fix the aggregate supply at $X$; in the second partial game the buyers contest this fixed prize in proportion to their bids and the aggregate bid in the equilibrium of this game is $\tilde{\mathcal B}(X)$. The analysis of these two partial games takes into account competition \emph{within} each side of the market. Equilibrium in bilateral oligopoly must take into account competition \emph{between} sellers and buyers and requires, for example, $\tilde{\mathcal B}(\tilde{\mathcal X}(B))=B$. When all traders have Cobb-Douglas preferences $\tilde{\mathcal X}(B)$ does not depend on $B$ and $\tilde{\mathcal B}(X)$ does not depend on $X$: whilst there is competition within each side of the market there is no strategic interdependence \emph{between} the sides of the market. The Cobb-Douglas assumption provides a tractable framework in which to explore the features of fully strategic trade but it misses perhaps the most interesting feature of bilateral oligopoly, the implications of which are investigated.

KW - strategic market game

KW - bilateral oligopoly

KW - Cobb-Douglas preferences

KW - aggregative games

U2 - 10.3917/rel.794.0089

DO - 10.3917/rel.794.0089

M3 - Article

VL - 79

SP - 89

EP - 110

JO - Louvain Economic Review

T2 - Louvain Economic Review

JF - Louvain Economic Review

SN - 0770-4518

IS - 4

ER -